To Be Finished
To Be Done, To Be Completed
intransitive verb, godan verb
Because the hiragana ends with an う sound, you know this word is a verb. The kanji means come to an end, so the verb vocab version is also about something ending: it means to be finished or to be done.
済む is used when something finishes or is resolved, often without further trouble, like 支払いが済む (the payment is completed). From this core idea of resolution, it also pops up in various other expressions about things coming to a close or being "enough."
For example, 気が済む means to feel satisfied with something such that you can get some issue out of your system, as in 気が済むまで泣く (cry till you feel better). Likewise, 〜で済む expresses that something on its own is sufficient, like 電話一本で済む (a single phone call is all it takes).
Since this word consists of a kanji with hiragana attached, you can bet that it will use the kun'yomi reading. You didn't learn that reading with this kanji, so here's a mnemonic to help you:
If something isn't done and you want it to be finished, your best bet is to sue (す) someone. Whether it's unresolved payments or uncompleted work, suing someone is the best way to ensure it gets finished. Of course, you will have to wait for the lawsuit itself to be settled first…
一回で済む
to be done in one go
これで済む
this is all you need, this alone takes care of it
〜円で済む
to cost only ~ yen
〜時間で済む
to finish in only ~ hours
気が済む
to be satisfied
手続きが済む
necessary procedures are completed
支払いが済む
payment is completed
用が済む
one's business is completed, one's task is taken care of
今やっと仕事が済んだところだよ。
My work finally wrapped up just now.
この作業が済んだら食堂に集まろうぜ！
Let's get together in the cafeteria once we're done with this work!
謝ったんだけど、「これは謝って済む問題じゃない」なんて言われちゃって、それで頭にきて彼の顔をひっぱたいちゃったのよね。
I apologized, but then he goes and says it's not something an apology can fix, so I got angry and slapped him in the face.